The US Supreme Court on Monday refused to take up an atheist challenge to the use of the phrase, “So help me God,” at the conclusion of the presidential oath of office during a president-elect’s inauguration.

The lawsuit initially asked a federal judge to block Chief Justice John Roberts from reciting “So help me God” while administering the oath in January 2009 to President-elect Obama. It also sought an order preventing two members of the clergy from conducting an invocation and benediction during the 2009 inauguration.

The complaint was later amended to seek an injunction against religious references in future inaugurations in 2013 and 2017.

At issue in the case was whether recitation of the phrase “So help me God” by the chief justice amounts to an unconstitutional endorsement of religion by government, in violation of the First Amendment’s establishment clause.

The lawsuit was filed by Michael Newdow, a Sacramento-based atheist, who had brought an earlier challenge to the recitation of the words “under God” during the Pledge of Allegiance in his daughter’s classroom each morning. That case reached the Supreme Court in 2004, where it was dismissed on grounds that Mr. Newdow lacked the necessary legal standing to raise the issue on behalf of his daughter.

The so-help-me-God suit was filed against the chief justice, potential prayer leaders, and inauguration committee members. It sought a court order barring references to God or religion during the ceremony.

In dismissing the lawsuit, the appeals court said that none of the individuals named in the suit had the power to redress the atheists’ underlying complaint since the president or president-elect has complete discretion to decide the content of the inauguration ceremony.

In urging the high court not to take up the case, Acting Solicitor General Neal Katyal wrote in his brief: “Because the content of the inaugural ceremony is entirely dependent on the president or president-elect’s wishes, only a judicial order running against the president or president-elect would result in the relief that [the atheists] seek. But [they] have not filed suit against the president or president-elect.”

Mr. Katyal added that the appeals court had emphasized that “a court would not have the authority to enter an injunction directly against the president in the exercise of his executive functions or against the president-elect (a private citizen) in the exercise of his personal religious beliefs.”

Chief Justice Roberts, who was named in the suit, did not take part in consideration of the case.